Find the largest Perfect Subtree in a given Binary Tree

Given a Binary Tree, the task is to find the size of largest Perfect sub-tree in the given Binary Tree.
Perfect Binary Tree – A Binary tree is Perfect Binary Tree in which all internal nodes have two children and all leaves are at the same level.


    /   \
   2     3
 /  \   /
4    5 6
Size : 3
Inorder Traversal : 4 2 5
The following sub-tree is the maximum size Perfect sub-tree 
 /  \
4    5

      /      \
   30         60
  /   \      /    \ 
 5    20   45      70
          /  \     /  \
         10   85  65  80
Size : 7
Inorder Traversal : 10 45 85 60 65 70 80

Approach: Simply traverse the tree in bottom up manner. Then on coming up in recursion from child to parent, we can pass information about sub-trees to the parent. The passed information can be used by the parent to do Prefect Tree test (for parent node) only in constant time. A left sub-tree need to tell the parent whether it is a Perfect Binary Tree or not and also need to pass max height of the Perfect Binary Tree coming from left child. Similarly, the right sub-tree also needs to pass max height of Prefect Binary Tree coming from right child.
The sub-trees need to pass the following information up the tree for finding the largest Perfect sub-tree so that we can compare the maximum height with the parent’s data to check the Perfect Binary Tree property.

  1. There is a bool variable to check whether the left child or the right child sub-tree is Perfect or not.
  2. From left and right child calls in recursion we find out if parent sub-tree if Prefect or not by following 2 cases:
    • If both left child and right child are perfect binary tree and have same heights then parent is also a Perfect Binary Tree with height plus one of its child.
    • If the above case is not true then parent cannot be perfect binary tree and simply returns max size Perfect Binary Tree coming from left or right sub-tree by comparing their heights.

Below is the implementation of the above approach:





// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Node structure of the tree
struct node {
    int data;
    struct node* left;
    struct node* right;
// To create a new node
struct node* newNode(int data)
    struct node* node = (struct node*)malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    return node;
// Structure for return type of
// function findPerfectBinaryTree
struct returnType {
    // To store if sub-tree is perfect or not
    bool isPerfect;
    // Height of the tree
    int height;
    // Root of biggest perfect sub-tree
    node* rootTree;
// Function to return the biggest
// perfect binary sub-tree
returnType findPerfectBinaryTree(struct node* root)
    // Declaring returnType that
    // needs to be returned
    returnType rt;
    // If root is NULL then it is considered as
    // perfect binary tree of height 0
    if (root == NULL) {
        rt.isPerfect = true;
        rt.height = 0;
        rt.rootTree = NULL;
        return rt;
    // Recursive call for left and right child
    returnType lv = findPerfectBinaryTree(root->left);
    returnType rv = findPerfectBinaryTree(root->right);
    // If both left and right sub-trees are perfect and
    // there height is also same then sub-tree root
    // is also perfect binary subtree with height
    // plus one of its child sub-trees
    if (lv.isPerfect && rv.isPerfect && lv.height == rv.height) {
        rt.height = lv.height + 1;
        rt.isPerfect = true;
        rt.rootTree = root;
        return rt;
    // Else this sub-tree cannot be a perfect binary tree
    // and simply return the biggest sized perfect sub-tree
    // found till now in the left or right sub-trees
    rt.isPerfect = false;
    rt.height = max(lv.height, rv.height);
    rt.rootTree = (lv.height > rv.height ? lv.rootTree : rv.rootTree);
    return rt;
// Function to print the inorder traversal of the tree
void inorderPrint(node* root)
    if (root != NULL) {
        cout << root->data << " ";
// Driver code
int main()
    // Create tree
    struct node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    // Get the biggest sizes perfect binary sub-tree
    struct returnType ans = findPerfectBinaryTree(root);
    // Height of the found sub-tree
    int h = ans.height;
    cout << "Size : " << pow(2, h) - 1 << endl;
    // Print the inorder traversal of the found sub-tree
    cout << "Inorder Traversal : ";
    return 0;



Size : 3
Inorder Traversal : 4 2 5

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